Non-invasive method and system for characterizing cardiovascular systems

ABSTRACT

The present disclosure uses physiological data, ECG signals as an example, to evaluate cardiac structure and function in mammals. Two approaches are presented, e.g., a model-based analysis and a space-time analysis. The first method uses a modified Matching Pursuit (MMP) algorithm to find a noiseless model of the ECG data that is sparse and does not assume periodicity of the signal. After the model is derived, various metrics and subspaces are extracted to image and characterize cardiovascular tissues using complex-sub-harmonic-frequencies (CSF) quasi-periodic and other mathematical methods. In the second method, space-time domain is divided into a number of regions, the density of the ECG signal is computed in each region and inputted into a learning algorithm to image and characterize the tissues.

CROSS-REFERENCE TO RELATED APPLICATION

This is a continuation application of U.S. patent application Ser. No.15/061,090, filed Mar. 4, 2016, now U.S. Pat. No. 9,655,536, which is acontinuation application of U.S. patent application Ser. No. 13/970,580,filed Aug. 19, 2013, now U.S. Pat. No. 9,289,150, which claims priorityto, and the benefit of, U.S. Provisional Patent Appl. No. 61/684,217,filed on Aug. 17, 2012, each of which is incorporated by referenceherein in its entirety.

BACKGROUND

The current algorithms employed in signal processing ofelectrocardiographic (ECG) signals are rudimentary and have limiteddiagnostic accuracy. In fact, validated and accepted ECG scoring systemslike the Selvester score have only a 71% accuracy in detecting aprevious myocardial infarction when compared to cardiac magneticresonance (CMR) imaging and the ECG is recognized as having significantlimitations in ruling in or ruling out an acute myocardial infarction.The ability of the ECG to detect left ventricular hypertrophy and otherconditions is also extremely limited. In fact, the ECG not recommendedto be used to rule out left ventricular hypertrophy in patients withhypertension. We claim that analysis of ECG data can be improved uponusing techniques to identify and quantify phase space changes tolocalize, image, and characterize architectural features and function ofcardiovascular and other mammalian tissues.

There are various time domain and frequency domain signal-processingtechniques which are being used for the analysis of physiologicalsignals to obtain more detailed information. While time domaintechniques are often used, they alone are incapable of quantifyingcertain fluctuation characteristics of a number of pathologies relatedto physiological signals. For example, traditional methods forperforming frequency-domain analysis of surface ECG signals, such as theFourier transform, are limited since they do not address the aperiodicrandom nature of biological and electromagnetic noise. For example,complex ECG waveforms with large variation in their morphologies havebeen shown to occur with the development of arrhythmias. Dominantfrequency analysis on ECG data can be problematic since non-lineardynamic systems can appear to generate random noise. Discrete fastFourier transforms and wavelet analysis have been shown experimentallyto be incapable of detecting deterministic chaos in the presence ofstrong periodicity which tends to obscure the underlying non-linearstructures.

BRIEF SUMMARY

The present disclosure generally relates to non-invasive methods andtechniques for characterizing mammalian cardiovascular systems. Morespecifically, the present disclosure relates to non-invasive methodsthat utilize electrocardiographic (ECG) phase space data to localize,image, and characterize architectural features and function of themyocardium and cardiovascular tissues.

The present disclosure uses physiological data, ECG signals as anexample, to evaluate cardiac structure and function in mammals. However,it is also claimed that other physiological data can similarly be usedto image and characterize other organ systems in mammals using a similarapproach. The present disclosure provides an improved and efficientmethod to image and characterize the heart using a high-resolution ECGdata. It is claimed that these ECG data can be used to identify,localize, and characterize cardiovascular tissues. ECG waveforms possesshigh-dimensional data with complex nonlinear variability that cannot beefficiently captured by traditional modeling techniques. Two approaches,namely model-based analysis and space-time analysis, are used to studythe dynamical and geometrical properties of ECG data. The first methoduses a modified Matching Pursuit (MMP) algorithm to find a noiselessmodel of the ECG data that is sparse and does not assume periodicity ofthe signal. After the model is derived, various metrics and subspacesare extracted to image and characterize cardiovascular tissues usingcomplex-sub-harmonic-frequencies (CSF) quasi-periodic and othermathematical methods. In the second method, space-time domain is dividedinto a number of regions (12 regions for ventricular tissue, see FIGS.10A and 10B and 6 regions for atrial tissues); the density of the ECGsignal is computed in each region and inputted into a learning algorithmto image and characterize the tissues.

As such, the present disclosure provides for a non-invasive system andmethod whereby ECG measurements can be taken and transformed tocharacterize and image architectural features of cardiovascular andother tissues. Further, the present disclosure provides a system andmethod to image (inverse ECG problem) and localize architecturalfeatures and function of cardiovascular tissues.

DESCRIPTION OF THE DRAWINGS

Exemplary embodiments of the present disclosure will hereinafter bedescribed in conjunction with the following drawing figures, whereinlike numerals denote like elements, and wherein:

FIGS. 1A and 1B show an overview of processes and algorithms to obtain aphase space representation and to derive a three-dimensional (3-D) modelof the heart;

FIG. 2 shows the steps of the model-based analysis to derive a noiselessmodel from ECG data using an MMP algorithm;

FIG. 3 presents process of phase space transformation;

FIG. 4 Illustrates the process of selecting the best dictionaries;

FIG. 5 illustrates model estimation process where sparse linearexpansion of selected atoms is used to mimic the ECG signal;

FIG. 6 illustrates one embodiment of a method whereby MMP can be used togenerate a 3-D vectorgram, where the blue trajectories are the raw ECGsignal plotted in 3 dimensions and red trajectories are the MMP model ofthe blue;

FIG. 7 shows a CSF trajectory derived from an MMP model of the ECG;

FIG. 8A shows a 3-D model of a heart where abnormalelectrical/anatomical features are highlighted in red. FIG. 8B is therepresentation of this data using a 17-segment cardiac anatomical map incommon use;

FIGS. 9A-9F present different dynamical behaviors of Rossler system fordifferent values of its parameter, c;

FIGS. 10A and 10B illustrate definitions of regions of the heart;

FIG. 11 demonstrates the ability of the disclosed methods to quantifyleft ventricular mass from only a high resolution ECG signal. ThisBland-Altman plot indicates that the quantification of left ventricularmass by ECG using the methods disclosed is comparable to that of cardiacmagnetic resonance (CMR) imaging, with clinically acceptable accuracy;

FIG. 12 demonstrates the ability of the disclosed methods to quantifyleft ventricular fibrosis from only a high resolution ECG signal. ThisBland-Altman plot indicates that the quantification of left ventricularfibrosis by ECG using the methods disclosed is comparable to that of CMRlate gadolinium enhancement (LGE) imaging, with clinically acceptableaccuracy; and

FIG. 13 demonstrates the ability of the disclosed methods to localizealterations in cardiac tissues, in this case hypertrophy/fibrosis, fromonly a high resolution ECG signal and the methods disclosed. Thisthree-by-three table indicates that the localization by ECG using themethods disclosed is comparable to that of CMR.

DETAILED DESCRIPTION

FIGS. 1A and 1B illustrate a high-level overview of the variousprocesses and algorithms implemented by the present disclosure to obtaina phase space representation and to derive a 3-D model of the heart.Referring to FIG. 1A, there is illustrated an operational flow diagramfor the regional analysis of myocardial perfusion. At 102, 100 to 700 ormore consecutive seconds of ECG data is gathered on each of single 12lead or 3 lead orthogonal leads. At 104, the signal is normalized andbaseline wander are removed using a modified moving average filter. At106, a Modified Matching Pursuit (MMP) algorithm may be used to find anoiseless model of the ECG data. At 108, delayed phase spacereconstruction is used to move the single or 3 lead or 12 lead ECG intoa 3 or higher dimensional space. At 110, the space-time domain isdivided into 12 regions or higher and the dynamical density of thesignal is computed for each region.

Dynamical signal density can be computed using non-Fourier or Fourier ndimensional fractional integral summation across all ECG leads on thederived model over the scan window. Typically the order of fractionalintegral could be −1.5 or −2.5 or any irrational, complex or realnumber.

Referring back to 106, the flow also proceeds to 112, where the modeledECG is split into the low energy complex sub harmonic subspace (CSF). At114, delayed phase space reconstruction is used to move the single or 3lead or 12 lead CSF ECG into a 3 or higher dimensional space. At 116,the space-time domain is divided into 12 Regions or higher and thedensity of the signal is computed for each region. At 118, the outputsof 110 and 116 are use to as 24 quantities (or higher) that are fed intoa nested sinusoidal Gaussians to generate 17 segments model for theregional analysis of myocardial perfusion.

Referring to FIG. 1B, there is a process for generating a geneticalgorithm. At 150, any cardiovascular imaging modality is input. At 152,specific image derived metrics such as Left/right ventricular massestimation, scar analysis using late gadolinium enhancement from cardiacmagnetic resonance imaging. Alternatively or additionally, at 154, anECG Space-Time based analysis is input. At 156, an evaluation ofSpace-Time density for different regions is performed. At 158, theoutput of 152 and/or 156 may be used to generate a genetic algorithm. At160, an imaging modality linked ECG model is created.

Aspects of FIGS. 1A and 1B are described in more detail below.

FIG. 2 illustrates the steps of the model-based analysis to derive anoiseless model from ECG data using an MMP algorithm. Step 204 shows thebaseline removal step, step 206 represents the phase spacetransformation step, step 208 presents the dictionary selection step,step 210 illustrates the model estimation step and step 212 demonstratesthe subspace extraction step. In FIG. 2, at 202, N-dimensional ECG isinput to a modified moving average filter to remove the baseline wanderfrom the data. The output then goes to a phase space transformationprocess at 206 in which a dynamically rich system (a system that canexhibit many different dynamical behaviors at different values of itsparameters) is synchronized with a physiological signal, in this caseECG data, to magnify its dynamical features. For example, Rossler is agood choice as it exhibits various behaviors for different values of itsparameters. The defining equations of Rossler system are as follows:

$\quad\left\{ \begin{matrix}{\overset{.}{x} = {{- y} - z}} \\{\overset{.}{y} = {x + {ay}}} \\{\overset{.}{z} = {b + {z\left( {x - c} \right)}}}\end{matrix} \right.$

where a, b, and c are some constants. For fixed values of a=b=0.1,Rossler system exhibits the following behavior for different values ofc.

TABLE 1 Value of c Dynamical Behavior Phase Space c = 4 Period-1 OrbitFIG. 9.A c = 6 Period-2 Orbit FIG. 9.B c = 8.5 Period-4 Orbit FIG. 9.C c= 8.7 Period-8 Orbit FIG. 9.D c = 13 Sparse Chaos FIG. 9.E c = 18Filled-in Chaos FIG. 9.F

The ECG data is synchronized with Rossler system and then a semi-optimalstate is identified that magnifies dynamical features of thephysiological signal under study, FIG. 3.

In accordance with FIG. 3, at 302, the ECG is synchronized with adynamical system. Next, at 304, a semi-optimal state that magnifies thedynamical features of the ECG is found. This creates a new ECG datasetwith magnified features at 306. Synchronization refers to phase spacebased synchronization of the information of the ECG system to theRossler system. The subspaces that arise from the differences betweenthe synchronization of these two systems are the magnifications of thedynamical features of the ECG. These subspaces comprise the new ECGdataset.

Referring again to FIG. 2, at 208, the obtained new dataset is then usedto find the best dictionary(ies) that can linearly span the input. Eachdictionary,

, is a family of waveforms

={φ_(i)|iεI} that is used to decompose the input. Various dictionariesare now available such as Wavelet Packets, Cosine Packets, Chirplets,and so on. In accordance with some implementations, complex exponentialsinusoids and Time-Frequency are used over complete dictionariessynchronized by a dynamically-rich family of post-transient Rosslertrajectories.

FIG. 4 illustrates the process of selecting the best dictionaries. At402, different dynamical features, such as Lyapunov exponent andcorrelation dimension, of the ECG or other physiological signal iscompared with a family of different dictionaries. At 404, thosedictionaries that have most similarity to the dataset is selected to beused for model estimation, i.e. the member atoms of the selecteddictionaries form the set of atoms that will be used in MMP. Thedynamical features of the ECG are compared with all the dictionaries andthe dictionaries are selected that have the most similarity with thedata

Referring again to FIG. 2, at 210, the next step is to find a sparsemodel (extracted from the selected dictionaries) for the physiologicalsignal under study. For example, MMP may be used, which is an iterativeprocess that, at each step, chooses the dictionary atom that bestcorrelates with the signal. This process continues until a pre-definedstopping condition occurs, such as if the number of terms exceeds athreshold and/or the distance of the model and the target in the searchspace is smaller than a threshold. Finally, the coefficients of theselected atoms are computed.

FIG. 5 sketches the process of model estimation using MMP. At 502, thecorrelation of the ECG dataset with all the atoms in the selecteddictionaries is computed. This information, along with the pre-evaluatedcross correlation of atoms (504) is used to pick the best atom in eachiteration in order to minimize a pre-defined cost function thatquantifies a distance in a metric space, such as mean absolute error ormean square error, between the model and the target waveform. After theaddition of each atom at 506, a stopping condition is consulted at 508to determine whether further iterations of the algorithm are necessary.This stopping condition could take into account factors such as thenumber of atoms already present in the model and the fit of the modelagainst the target waveform. If the stopping condition has beensatisfied at 508, the algorithm proceeds to 510 to perform a calculationof the coefficients of the atoms. These coefficients are reclusivelycalculated using information captured during the iteration of thealgorithm in order to optimize the fit of the model against the inputwaveform. The process begins with reading pre-computed atom correlationsand computing the correlations between the input waveform and the atoms.Atoms are iteratively added until the stopping condition is satisfied,at which point the coefficients are calculated

Returning to FIG. 2, at 212, different subspaces are extracted from thederived model. Various subspaces, namely CSF trajectory, quasi-periodicand chaotic subspaces, low/high-energy subspace, and fractionalderivative of the low/high-energy subspace are extracted from thederived model; however, possible subspaces that could be extracted arenot limited to these examples. Each of which represents a dynamicalabnormality in the tissue architecture, structure and function.

The last 20% of the selected atoms are used to form a “low energysubspace” signal corresponding to each of the leads. These low energysignals can be called x(t), y(t), and z(t) assuming 3 leads.

There are various time domain and frequency domain signal processingtechniques used for the analysis of physiologic signals to obtain moredetailed information. CSF exist in many physiological signals, not justthe cardiac signals presented, and are likely indicative of otherpathophysiological processes not otherwise detectable using prior artmethods.

3-D Visualization

The output obtained after applying the MMP algorithm on the ECG or otherphysiological signal, can be represented as a 3-D phase space plot, asshown in FIG. 6. The illustrated 3-D phase space plot illustratescardiac electrical conduction patterns, and associated alterations intissue architecture, structure and function. This invention can be used,for example, to detect hypertrophy, ischemia, scar, abnormal electricalchannel function (channelopathies) and other forms of inherited oracquired heart disease in mammals. In addition, this method can be usedto assess the effects (positive and negative) of various interventionsthat include medications, toxins, chemotherapeutic agents, surgicalprocedures, and other interventional procedures such as ablation,pacing, shocks and electrical therapies, and genetic therapies.

The 3-D phase space plot localizes the presence of CSF related toaltered tissue. For example, the CSF for the heart can be measured as atime delay and as a 3-D trajectory in the atrial and ventricularsub-spaces. CSF trajectory is associated with those components of theECG not captured by the dictionary, i.e. there is no linear combinationof the atoms of the selected dictionaries that can represent the CSFtrajectory. FIG. 7 shows a CSF trajectory derived from an MMP model ofan ECG.

Examples of the 3-D phase space plot are shown in FIGS. 8-10. FIG. 8Ashows a 3-D model of a heart where abnormal electrical/anatomicalfeatures are highlighted in red. FIG. 8B is the representation of thisdata using a 17-segment cardiac anatomical map in common use (see FIGS.10A and 10B). FIGS. 9A-9F present different dynamical behaviors ofRossler system for different values of its parameter, c. FIGS. 10A and10B illustrate definitions of regions of the heart.

The 3-D phase space plot of the present disclosure may be displayed byany type of computing device, including, but not limited to, desktopcomputers, workstation computers, server computers, cloud computingdevices, tablet devices, smart phones, and mobile computing devices.

A methodology will now be described below for producing output from analgorithm that correlates with clinical parameters describing tissuearchitecture, structure and function. Descriptive attributes in thatclass include left ventricular mass and fibrosis as measured using CMRLGE imaging. As indicated in FIGS. 11 and 12, cardiac mass and fibrosiscan be reliably detected and quantified using the implementations of thepresent disclosure. For example, the anatomic location of these changescan also be reliably determined using the disclosed methods, as shown bythe data in FIG. 13.

FIG. 11 provides data related to the blind performance of the precedingformula for predicting left ventricular mass from just a high resolutionECG signal, compared to CMR, a method for assessing left ventricularmass. These data indicate that the methods disclosed provide a leftventricular mass value that is sufficiently close to the actual CMRvalue, to support the use of ECG data analyzed using the methodsdisclosed alone to quantify cardiac mass.

FIG. 12 provides data related to the blind performance of the precedingformula for predicting fibrosis from just a high resolution ECG signal,compared to CMR, a method for assessing fibrosis, assessed as percentLGE. These data indicate that the methods disclosed provide an estimateof fibrosis that is sufficiently close to the actual CMR value, tosupport the use of ECG data analyzed using the methods disclosed aloneto estimate the percent of cardiac fibrosis.

The algorithm utilizes space-time densities computed using thespace-time analysis method to create a predominantly time agnosticfeature set representative of the dynamics of the signal propagationthrough tissue. The space-time metrics are then linked with clinicaldata sets, for example left ventricular mass, using a genetic learningalgorithm. The subsequent result can then be used in independent datasets to reliably characterize the tissues of interest as shown in FIGS.11, 12 and 13. Exemplar formulas for the clinical parameters related tothese specific examples follow. It is explicitly noted that the formulasbelow are being provided solely as examples, and should not be construedas limiting the disclosure, as recited in the claims, as variations,modifications, and adaptations of the equations below to achieve thefunctions of the present disclosure are considered to be within thescope of the appended claims.

Example Formulas

Estimate of percent fibrosis as measured using CMR LGEimaging=((cosh((gauss((SD1−SD2))))/(gauss((gauss((SD3/SD4*SD5)))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5)))))))))))+(((gauss((gauss(SD7)))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3̂2)*SD7*(gauss(SD11))))/(SD1*SD2)))))))))+(SD3+SD4+(SD6*(gauss((SD2*SD4))))+((SD5*(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))/SD3)+(gauss((SD1−(SD3*SD8))))+(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))−((cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5)))))))))))−((gauss((gauss(SD7)))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3̂2)*SD7*(gauss(SD11))))/(SD1*SD2)))))))))*gauss(((SD3+SD4+(SD6*(gauss((SD2*SD4))))+((SD5*(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))/SD3)+(gauss((SD1−(SD3*SD8))))+(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))̂2+((cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD3/SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5)))))))))))̂2−((gauss((gauss(SD7)))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3̂2)*SD7*(gauss(SD11))))/(SD1*SD2)))))))))̂2)/(((gauss((gauss(SD7))))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3̂2)*SD7*(gauss(SD11))))/(SD1*SD2)))))))))+(SD3+SD4+(SD6*(gauss((SD2*SD4))))+((SD5*(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6)))))/SD3)+(gauss((SD1−(SD3*SD8))))+(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))+((cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD3/(SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5)))))))))))+(SD3+SD4+(SD6*(gauss((SD2*SD4))))+((SD5*(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))/SD3)+(gauss((SD1−(SD3*SD8))))+(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))̂2+((cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD3/(SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5)))))))))))̂2)))/cosh(((gauss((gauss(SD7))))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3̂2)*SD7*(gauss(SD11))))/(SD1*SD2)))))))))/cosh(((gauss((gauss(SD7))))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3̂2)*SD7*(gauss(SD11))))/(SD1*SD2)))))))))̂2/((SD3+SD4+(SD6*(gauss((SD2*SD4))))+((SD5*(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))/SD3)+(gauss((SD1−(SD3*SD8))))+(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))*((cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD3/(SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5)))))))))))*gauss(((cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD3/(SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5)))))))))))̂3*gauss(((gauss((gauss(SD7))))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3̂2)*SD7*(gauss(SD11))))/(SD1*SD2)))))))))+(SD3+SD4+SD6*(gauss((SD2*SD4))))+((SD5*(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))/SD3)+(gauss((SD1−(SD3*SD8))))+(gauss(((SD7*SD3)/((SD2*SD6)−(SD3*SD6))))))+(cosh((gauss((SD1−SD2)))))/((gauss((gauss((SD3/(SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5)))))))))))/((gauss((gauss(SD7))))/((SD8*SD7)+(gauss(((gauss(SD9))+(gauss((((SD10*SD8)+((SD3̂2)*SD7*(gauss(SD11))))/(SD1*SD2)))))))))−((cosh((gauss((SD1−D2)))))/((gauss((gauss((SD3/(SD4*SD5))))))*(gauss((cosh((gauss((SD6+(SD12/(SD6*SD5))))))))))))))))SD=signal densityEstimation of left ventricular mass as measured usingCMR=((SD9+(SD4*(cosh(SD5))))/((gauss(SD5))+(gauss(((SD1*SD10*SD7)/((((SD1*SD9*SD10*SD11*SD4)−SD11)−(SD9*SD10*SD12*SD7))−((SD1̂2)*SD10*SD5)))))))+((((SD4+(SD1*SD2)+(SD5*SD3)+(SD1*SD2*SD5))−SD8)/(cosh(((gauss((SD2+(SD4/SD1))))−(cosh((gauss((gauss(((SD1*SD3)+((−SD3)/SD5))))))))))))*(SD2+(SD1*SD2)+(SD3/(SD2+(SD8*SD3*(gauss(((SD2̂2)/SD6))))+(gauss(SD5))+(gauss((SD1/SD4))))))*((cosh(SD6))+(cosh((gauss((cosh(SD7))))))+(cosh((((cosh((gauss(SD6))))2)+((cosh((gauss(SD6))))*(cosh((gauss((gauss((gauss(SD6)))))))))+(cosh((gauss(SD9))))))))−((SD9+(SD3*(cosh(SD5))))/((gauss(SD5))+(gauss(((SD1*SD10*SD7)/((((SD1*SD9*SD10*SD11*SD4)−SD11)−(SD9*SD10*SD12*SD7))−((SD1̂2)*SD10*SD5)))))))̂2*(((SD3+(SD1*SD2)+(SD5*SD3)+(SD1*SD2*SD5))−SD8)/(cosh(((gauss((SD2+(SD4/SD1))))−(cosh((gauss((gauss(((SD1*SD3)+((−SD3)/SD5)))))))))))))/((SD2+(SD1*SD2)+(SD3/(SD2+(SD8*SD3*(gauss(((SD2̂2)/SD6))))+(gauss(SD5))+(gauss((SD1/SD4))))))̂2+(SD2+(SD1*SD2)+(SD3/(SD2+(SD8*SD3*(gauss(((SD2̂2)/SD6))))+(gauss(SD5))+(gauss((SD1/SD4))))))̂3*gauss((((SD3+(SD1*SD2)+(SD5*SD3)+(SD1*SD2*SD5))−SD8)/(cosh(((gauss((SD2+(SD4/SD1))))−(cosh((gauss((gauss(((SD1*SD3)+((−SD3)/SD5))))))))))))*(SD2+(SD1*SD2)+(SD3/(SD2+(SD8*SD3*(gauss(((SD2̂2)/SD6))))+(gauss(SD5))+(gauss((SD1/SD4))))))/(((SD9+(SD3*(cosh(SD5))))/((gauss(SD5))+(gauss(((SD1*SD10*SD7)/((((SD1*SD9*SD10*SD11*SD4)−SD11)−(SD9*SD10*SD12*SD7))−((SD1̂2)*SD10*SD5)))))))̂2)))SD=signal density

Ischemia of cardiac tissues is linked to the development ofphysiological changes that could alter complex sub-harmonics and resultsin variable and high dimensional changes. FIG. 7 illustrates oneembodiment of a method whereby MMP is used to generate a 3-D vectorgramto localize, image, and characterize aberrant architectural features ofthe myocardium based on CSF identification, quantification andlocalization.

In accordance with the present disclosure, physiological andpathophysiological features of tissues are modeled accurately andeffectively using fractional derivatives. In contrast, classical integerderivative-based models capture these phenomena only approximately ornot at all. Traditional integer order derivatives depend only on thelocal behavior of a function, while fractional derivatives depend on thewhole history of the function. In this embodiment, there is utilized amethod for detecting beat to beat complex sub-harmonic structures in theECG based on digital differentiation and integration of fractionalorder. Since these signals are mathematically modeled as a linearcombination of the selected atoms, they can be differentiated andintegrated of fractional order. Let x′(t), y′(t), and z′(t) be theirinteger order derivatives respectively, these derivatives and thereratios measure instability only at a local point of the signal andtherefore are poor measures of stability for long complex ECG signalswith significant beat-to-beat variability. An alternative to an integerderivative is the use of a fractional calculus to detect abnormal CSFsignals in a physiological signal based on its past history.

There are two concepts regarding the low-energy component subspace (madefrom the last 20% terms found by MMP) that are interesting and useful.First, the fractional derivative of this component can be noiselesslyobtained, since it is a linear combination of selected atoms, and thisfractional derivative can be useful to localize, image, and characterizearchitectural features of tissues. In addition, there are some usefulfractional properties to consider. Thus suppose that x(t),y(t), and z(t)are respectively the X, Y, and Z coordinates of the low-energy componentand let x^(α)(t), y^(α)(t), and z^(α)(t) be their irrational fractionalderivative of order α that can be any real(or complex) number. Then themagnitude of these irrational fractional derivatives can indicateinstability when large and positive. Consider the regions when theirrational fractional derivatives are positive, in such regions, the lowenergy re-entrant wavelets that signify alterations in tissuearchitecture and, or function.

The phase space plot information cannot be easily superimposed on a 3-Drepresentation of a given tissue since physiological function isvariable across individuals. To overcome this problem, intrinsic phasespace imaging does not use the interference in the phase plane ofinterest. Noiseless subspaces allow the recording of the phase of thesewaves. In cardiac tissues the amplitude resulting from this interferencecan be measured, however the phase of the orthogonal leads still carriesthe information about the structure and generates geometrical contrastin the image, thus the name phase-contrast imaging.

In phase-based imaging, phase-contrast takes advantage of the fact thatdifferent bioelectric structures have different impedances, and sospectral and non-spectral conduction delays and bend the trajectory ofphase space orbit through the heart by different amounts. These smallchanges in trajectory can be normalized and quantified on a beat-to-beatbasis and corrected for lead placement and the normalized phase spaceintegrals can be mapped to a geometric mesh using a genetic algorithm tomap 17 myocardial segments in the ventricle to various tomographicimaging modalities of the heart from retrospective data (exemplarformulas for 3 of the 17 regions below). FIG. 13 provides data relatedto the blind performance of localizing tissue abnormalities from just ahigh resolution ECG signal, compared to CMR, an accurate localizationmethod. These data indicate that the methods disclosed provide areliable means to localize the anatomic location of the tissuealteration. Thus, the disclosed method can be used to assess the effects(positive and negative) of various interventions that altercardiovascular tissue architecture and, or function includingmedications, toxins, chemotherapeutic agents, surgical procedures, andother interventional procedures such as ablation, pacing, shocks andelectrical therapies, and genetic therapies.

basal anteriorsegment=cosh(SD10)−gauss(SD11*SD12*SDCSF1+0.005778*SDCSF2*SD6*SD10*SDCSF3−6.749*SDCSF4*(gauss(((((0.0735+(0.3203*SDCSF5*(gauss((30.33*SD8*(gauss(((SD8+((61.1*SDCSF6*SDCSF7)/((SDCSF8*(gauss((9.666*SD1*SDCSF9*SDCSF1))))+(SDCSF11*(gauss((9.666*SD1*SDCSF9*SDCSF10))))+(SDCSF8*SDCSF12*SDCSF6*SDCSF7*(gauss((9.666*SD1*SDCSF9*SDCSF10)))))))−(gauss((gauss(SDCSF7)))))))))))−(2.994*SD10))−(17.03*(gauss((6.882*(gauss(((SD8+((61.1*SDCSF6*SDCSF7)/((SDCSF8*(gauss((9.666*SD1*SDCSF9*SDCSF10))))+(SDCSF11*(gauss((9.666*SD1*SDCSF9*SDCSF10))))+(SDCSF8*SDCSF12*SDCSF6*SDCSF7*(gauss((9.666*SD1*SDCSF9*SDCSF10))))))−(gauss((gauss(SDCSF7))))))))))))/SD1)))*gauss(SD1))mid infecolateralsegment=gauss(7.44069511*SD1+6*SD1*SD2+−2.51202217109399*SD3/SD4+SD5*SD6/(SD7*SD8)−SD3*SD8*SD9−0.8372177305*SD1*SD4)apical inferiorsegment=gauss((SD2*SD3−0.2868*SD3−0.2308*gauss(14.35*SD2−9.859*SD4))/SD1̂2*((0.8889*((((gauss(((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8̂2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss(SD10*(gauss(SDCSF12))*((gauss((((SDCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gauss(((SD1−(gauss((((SD3/(SD1+(SD1*SD7)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8̂2)))))))),/(gauss(SD8)))+(0.8999*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(−5.393−SD5))))))/1.8))+((SD1*((((gauss(((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(/SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD5̂2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss((((SDCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gauss(((SD1−(gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8̂2))))))))/(gauss(SD8)))+(0.8999*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(−5.393−SD5))))))/1.8))/SD8)+((35.21*SDCSF2*((((gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8̂2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss((((SDCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gauss(((SD1−(gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8̂2))))))))/(gauss(SD8)))+(0.8999*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(−5.393−SD5))))))/1.8))/SD5)+((−5997000*SDCSF3*((((gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8̂2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss((((SDCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gauss(((SD1−(gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss(SD8̂2))))))))/(gauss(SD8)))+(0.8999*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(−5.393−SD5))))))/1.8))/SD11))+((0.8889*((((gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8̂2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.95))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss((((SDCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gauss(((SD1−(gauss((((SD3/(SD1+(SD1*SD7)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8̂2)))))))/(gauss(SD8)))+(0.8999*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(5.393−SD5))))))/1.8))+((SD1*((((gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7)))−(SD1*SD3)))*(gauss((SD8̂2))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss((((SDCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gauss(((SD1−(gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8̂2))))))))/(gauss(SD8)))+(0.8999*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(−5.393−SD5))))))/1.8))/SD8)+((35.21*SDCSF2*((((gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8̂2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss((SD10*(gauss(SDCSF12))*((gauss((((SDCSF10+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gauss(((SD1−(gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(0.8999*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(−5.393−SD5))))))/1.8))/SD5)+(−5997000*SDCSF3*((((gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3))))*(gauss((SD8̂2))))+(((gauss((SDCSF4/(gauss(((SD9+SDCSF10)−1.959))))))*(gauss(SD10*(gauss(SDCSF12))*((gauss((((SDCSF10)+(13.62*(gauss(SDCSF12))))−1.365)/SDCSF4)))/SDCSF2))))*(gauss(((SD1−(gauss((((SD3/(SD1+(SD1*SD5)))+(1.764e−6*SD1*(SD5̂2)*(SD6/SD7))+(SD5*((−1*SD1)̂2)*(SD6/(SD5*SD7))))−(SD1*SD3)))))/(SD6*(gauss((SD8̂2)))))))/(gauss(SD8)))+(0.8999*(gauss((((((SDCSF8+SD11)−12.05)−(SD1*SD12*SDCSF1))−(12.93*SD1*SD12))/(−5.393−SD5))))))/1.8))/SD11))̂3))SD=signal densitySDCSF=signal density complex-sub-harmonic-frequencies

In the second method, space-time domain is divided into a number ofregions (for example, 12 regions for ventricular and 6 regions foratrial tissues); the density of the baseline-removed ECG signal iscomputed in each region. These values contain specific information aboutthe non-linear variability of the physiological signal, specifically theECG signal, that are linked to an alteration in tissue architecture and,or function. The calcium ion (Ca++) is a universal intracellularmessenger. In muscle, Ca++ is central to contractile force activation.Ca++ is also important for temporal and spatial alterations in actionpotentials, modulation of contractile function due to systemicresistance (blood pressure), energy supply-demand balance (includingmitochondrial function), cell death (apoptosis), and transcriptionregulation. It has been hypothesized that Ca++-dependent ion pumpvariability occurs aperiodically in pathological cardiac myocytes, thiscreates significant microvolt beat-to-beat variations in the ECG signalsand possibly other physiological signals (e.g., arterial pulsewaveform). Variations in the ECG or other physiological signal can bemeasured and localized by linking the space time density structures totissues of interest (for example, the 12 ventricular and 6 atrialregions). It should be noted a simple derivative or its ratios is notsufficient to characterize space-time density structures over manycardiac cycles.

For the cardiac ventricle the 12 quantities are input to a geneticalgorithm and are modeled to link 17 myocardial segments in theventricle (see FIGS. 10A and 10B) to various tomographic imagingmodalities of the heart (collected data). The region boundaries areagnostic to the physiological signal, for example the clinical ECGlandmarks commonly referred to as P, Q R, S, T, and U waves. The resultis 17 nonlinear nested sinusoidal Gaussian equations for the ventriclethat link the 12 dimensional space-time density metrics to tomographicimaging modalities of the collected data. These same ECG metrics can beused to localize, image, and characterize architectural features andfunction of tissues, in the example, the heart.

Ectopic foci can produce dynamic spatial dispersion of repolarizationand conduction block, initiating re-entrant arrhythmias. Dynamic spatialdispersion of repolarization in atrial and ventricular tissues can bedetected and localized using space-time analysis on the described 6atrial and 12 ventricular 6 regions. These quantities are then inputtedinto a genetic algorithm and are modeled to link regions of interest tovarious tomographic images from collected data.

Spatial changes in the phase space matrix can be can be computed usingnon-Fourier or Fourier multi-dimensional fractional integral summationacross all ECG leads on the derived model to generate the dynamicalspace-time density metrics. For cardiac ventricular tissue these metricsare modeled using a genetic algorithm to link 17 non-linear nestedsinusoidal Gaussian equations previously described to the commonly used17-segment model shown in FIGS. 10A and 10B. Segments with alteredarchitectural features and, or function are identified and the degree ofabnormality quantified, permitting assigning a probability of the saidtissue having a pathophysiological abnormality that can be characterizedas hypertrophy, atrophy, scar, ischemia, edema, fibrosis or anothercondition. For example, the probability of regional ischemia in aventricular segment can be identified and quantified as shown in FIGS.8A and 8B.

Having thus described several embodiments of the present disclosure, itwill be rather apparent to those skilled in the art that the foregoingdetailed disclosure is intended to be presented by way of example only,and is not limiting. Many advantages for non-invasive method and systemfor localization, imaging, and characterization of architecturalfeatures and function of tissues have been discussed herein. Variousalterations, improvements, and modifications will occur and are intendedto those skilled in the art, though not expressly stated herein. Thesealterations, improvements, and modifications are intended to besuggested hereby, and are within the spirit and the scope of the presentdisclosure. Additionally, the recited order of the processing elementsor sequences, or the use of numbers, letters, or other designationstherefore, is not intended to limit the claimed processes to any orderexcept as may be specified in the claims. Accordingly, the presentdisclosure is limited only by the following claims and equivalentsthereto.

1. A method for localizing and characterizing both the architecturalfeatures and function of cardiovascular tissues, comprising the steps ofobtaining ECG data for the heart; processing the ECG data to localize,image, and characterize architectural features and function of tissueswithout use of other measuring devices or invasive procedures; and usingphase information to determine a location of an architectural feature orfunction of the tissues to display an abnormality associated with thetissues in a 3-D image.